Adaptive Bayesian density estimation with location-scale mixtures

W.T. Kruijer, J. Rousseau, A. van der Vaart

Research output: Contribution to journalArticleAcademicpeer-review

44 Citations (Scopus)

Abstract

We study convergence rates of Bayesian density estimators based on finite location-scale mixtures of exponential power distributions. We construct approximations of β-Hölder densities be continuous mixtures of exponential power distributions, leading to approximations of the β-Hölder densities by finite mixtures. These results are then used to derive posterior concentration rates, with priors based on these mixture models. The rates are minimax (up to a logn term) and since the priors are independent of the smoothness the rates are adaptive to the smoothness.
Original languageEnglish
Pages (from-to)1225-1257
JournalElectronic Journal of Statistics
Volume4
DOIs
Publication statusPublished - 2010

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